I have been living without time from a few years and it is a bliss. I have removed time from my laptop. For android mobile, I couldn't find a reliable way to remove time and I used to change timezone to a random zone. With Xposed framework we can remove clock from lock screen and status bar.
Before proceeding, make sure your phone is [rooted][] and [Xposed framework][xposed] is installed.
### Remove Clock From LockScreen
To remove clock from lockscreen, download [Lock screen widgets][lsw] module and activate it.
If you open it, it has an option to hide date and time.

### Remove Time From StatusBar
To remove clock from status bar, you have to install [GravityBox][]. Open GravityBox and goto statusbar settings

If you are already using CyanogenMod, there is an option to hide time in settings.

Once you do this, you will have a neat lockscreen without any time on it.